基于SCILAB的多精度算法研究与实现

Research and implementation of multi-precision algorithm based on SCILAB

当前,通用处理器一般支持64位浮点运算,在大规模和长时程数值计算中,由于浮点运算的舍入误差累积效应,可能导致数值结果不可信。因此,有效控制误差,设计高精度、高效可靠的浮点数值算法至关重要。基于SCILAB软件平台,通过使用无误差变换和double-double数据格式,实现了高精度的算法库。对幂指数、Bernstein和Chebyshev基多项式函数估值,在Intel平台和国产飞腾处理器平台上进行了数值实验,实验结果证实了该高性能数值算法库的有效性。该多精度算法库具有独立知识产权,可有效应用于国产自主可控处理器平台,为国家重大科研项目提供技术支持。

Currently,general-purpose processors generally support 64-bit floating point operations.In large-scale and long-time scientific numerical calculation,the cumulative effect of rounding errors in floating-point operations may lead to unreliable numerical results.Therefore,to effectively control errors,designing high-precision,efficient and reliable floating-point numerical algorithms is very important.By using error-free transform and double-double format,this paper realizes a high-precision mathematics library based on SCILAB software platform.The evaluation of the polynomials in power basis,Bernstein form and Chebyshev basis is carried out on the Intel platform and the domestic FT processor platform.The results prove the validity of our proposed high-precision mathematics library.This library has independent intellectual property right and can run on the self-dependent and manageable domestic processor,which will support the national high technology research.